Ambiental cluster

head(readstate)

multi_cluster <- readstate %>%
  group_by(state,months) %>%
  summarise(MaximumTemperature= max(MaximumTemperature),
            MinimumTemperature= min(MinimumTemperature),
            Precipitation = mean(Precipitation), 
            AverageTemperature = mean(AverageTemperature),
            PalmerDroughtSeverityIndexPDSI = mean(PalmerDroughtSeverityIndexPDSI)
            )

`summarise()` has grouped output by 'state'. You can override using the
`.groups` argument.

multi_cluster <- multi_cluster %>%
  group_by(state) %>%
  summarise(max(MaximumTemperature), min(MinimumTemperature), mean(Precipitation)
            , mean(AverageTemperature), mean(PalmerDroughtSeverityIndexPDSI))


multi_cluster[multi_cluster$state=="Alaska",6] <- 0
which(is.na(multi_cluster))

integer(0)

  dataset.e <- dist(multi_cluster, method = 'euclidean') #no method -> euclidean (default)

Warning in dist(multi_cluster, method = "euclidean") :
  NAs introduced by coercion

  dataset.es <- hclust(dataset.e, method = 'single') 
  dataset.ea <- hclust(dataset.e, method = 'average')
  dataset.ec <- hclust(dataset.e, method = 'complete')
  dataset.ew <- hclust(dataset.e, method = 'ward.D2')
  
  #plot of dendograms
  par(mfrow=c(1,3))
  plot(dataset.es, main='euclidean-single', hang=-0.1, xlab='', labels=F, cex=0.6, sub='')
  plot(dataset.ec, main='euclidean-complete', hang=-0.1, xlab='', labels=F, cex=0.6, sub='')

  plot(dataset.ea, main='euclidean-average', hang=-0.1, xlab='', labels=F, cex=0.6, sub='')

  plot(dataset.ew, main='euclidean-ward', hang=-0.1, xlab='', labels=F, cex=0.6, sub='')

  
  #cutting dendograms: (with k=2 fixed)
  cluster.ec <- cutree(dataset.ec, k=3) # euclidean-complete:
  cluster.ea <- cutree(dataset.ea, k=3) # euclidean-average:
  cluster.es <- cutree(dataset.es, k=3) # euclidean-simple:
  cluster.ew <- cutree(dataset.ew, k=3) # euclidean-simple:

  
  
  # Let's give a mark to the algorithms: did they aggregate coherently with
  # the dissimilarity matrix or not?
  # compute the cophenetic matrices 
  coph.es <- cophenetic(dataset.es)
  coph.ec <- cophenetic(dataset.ec)
  coph.ea <- cophenetic(dataset.ea)
  coph.ew <- cophenetic(dataset.ew)

  
  # compute cophenetic coefficients (<-> corr(D,C)) D:dist mat; C:coph dist mat
  es <- cor(dataset.e, coph.es)
  ec <- cor(dataset.e, coph.ec)
  ea <- cor(dataset.e, coph.ea)
  ew <- cor(dataset.e, coph.ew)

  
  c("Eucl-Single"=es,"Eucl-Compl."=ec,"Eucl-Ave."=ea, "Eucl-War."=ew)

Eucl-Single Eucl-Compl.   Eucl-Ave.   Eucl-War. 
  0.5224238   0.6759758   0.7415526   0.6729451 

Ha più senso utilizzare Euclidean-Average con k=3

library(plotly)
us_data <- map_data("state")
df <- data.frame(
  state = tolower(multi_cluster$state),
  values = cluster.ew
)

library(usmap)
plot_usmap(data = df) + labs(title = "Multivariate cluster (all cov)")

#Now standardize data

std_multi_cluster<- scale(multi_cluster[,-1])
dataset.e <- dist(std_multi_cluster, method = 'euclidean') #no method -> euclidean (default)

  dataset.es <- hclust(dataset.e, method = 'single') 
  dataset.ea <- hclust(dataset.e, method = 'average')
  dataset.ec <- hclust(dataset.e, method = 'complete')
  dataset.ew <- hclust(dataset.e, method = 'ward.D2')
  
  #plot of dendograms
  par(mfrow=c(1,3))
  plot(dataset.es, main='euclidean-single', hang=-0.1, xlab='', labels=F, cex=0.6, sub='')
  plot(dataset.ec, main='euclidean-complete', hang=-0.1, xlab='', labels=F, cex=0.6, sub='')

  plot(dataset.ea, main='euclidean-average', hang=-0.1, xlab='', labels=F, cex=0.6, sub='')

  plot(dataset.ew, main='euclidean-ward', hang=-0.1, xlab='', labels=F, cex=0.6, sub='')

  
  #cutting dendograms: (with k=2 fixed)
  cluster.ec <- cutree(dataset.ec, k=3) 
  cluster.ea <- cutree(dataset.ea, k=4) # va bene 3 o 4
  cluster.es <- cutree(dataset.es, k=3) 
  cluster.ew <- cutree(dataset.ew, k=4) #va bene 3 o 4

  
  
  # Let's give a mark to the algorithms: did they aggregate coherently with
  # the dissimilarity matrix or not?
  # compute the cophenetic matrices 
  coph.es <- cophenetic(dataset.es)
  coph.ec <- cophenetic(dataset.ec)
  coph.ea <- cophenetic(dataset.ea)
  coph.ew <- cophenetic(dataset.ew)

  
  # compute cophenetic coefficients (<-> corr(D,C)) D:dist mat; C:coph dist mat
  es <- cor(dataset.e, coph.es)
  ec <- cor(dataset.e, coph.ec)
  ea <- cor(dataset.e, coph.ea)
  ew <- cor(dataset.e, coph.ew)

  
  c("Eucl-Single"=es,"Eucl-Compl."=ec,"Eucl-Ave."=ea, "Eucl-War."=ew)

Eucl-Single Eucl-Compl.   Eucl-Ave.   Eucl-War. 
  0.6191115   0.6911089   0.7474144   0.5645727 

Anche in questo caso E-A ma k=2 migliore (ignoreremo ciò e usiamo k=3)

cluster_index

      state            temp_min temp_max temp_avg prec pdsi multi_all_ward
 [1,] "Alabama"        "1"      "1"      "3"      "3"  "1"  "1"           
 [2,] "Alaska"         "2"      "3"      "1"      "1"  NA   "2"           
 [3,] "Arizona"        "1"      "1"      "3"      "2"  "3"  "3"           
 [4,] "Arkansas"       "1"      "1"      "3"      "1"  "2"  "1"           
 [5,] "California"     "1"      "1"      "3"      "1"  "3"  "3"           
 [6,] "Colorado"       "3"      "1"      "2"      "1"  "3"  "2"           
 [7,] "Connecticut"    "1"      "1"      "2"      "1"  "1"  "4"           
 [8,] "Delaware"       "1"      "1"      "2"      "3"  "1"  "4"           
 [9,] "Florida"        "1"      "1"      "3"      "1"  "3"  "1"           
[10,] "Georgia"        "1"      "1"      "3"      "3"  "1"  "1"           
[11,] "Idaho"          "2"      "2"      "1"      "1"  "3"  "2"           
[12,] "Illinois"       "1"      "1"      "2"      "1"  "2"  "4"           
[13,] "Indiana"        "1"      "1"      "2"      "1"  "2"  "4"           
[14,] "Iowa"           "3"      "2"      "1"      "1"  "2"  "2"           
[15,] "Kansas"         "1"      "1"      "2"      "1"  "2"  "1"           
[16,] "Kentucky"       "1"      "1"      "2"      "1"  "2"  "4"           
[17,] "Louisiana"      "1"      "1"      "3"      "1"  "2"  "1"           
[18,] "Maine"          "3"      "3"      "1"      "1"  "1"  "2"           
[19,] "Maryland"       "1"      "1"      "2"      "3"  "2"  "4"           
[20,] "Massachusetts"  "1"      "1"      "2"      "1"  "1"  "4"           
[21,] "Michigan"       "3"      "3"      "1"      "1"  "2"  "2"           
[22,] "Minnesota"      "3"      "2"      "1"      "1"  "2"  "2"           
[23,] "Mississippi"    "1"      "1"      "3"      "1"  "2"  "1"           
[24,] "Missouri"       "1"      "1"      "2"      "1"  "2"  "4"           
[25,] "Montana"        "2"      "2"      "1"      "1"  "3"  "2"           
[26,] "Nebraska"       "3"      "2"      "2"      "1"  "2"  "2"           
[27,] "Nevada"         "1"      "1"      "2"      "1"  "3"  "3"           
[28,] "New Hampshire"  "3"      "3"      "1"      "1"  "1"  "2"           
[29,] "New Jersey"     "1"      "1"      "2"      "1"  "1"  "4"           
[30,] "New Mexico"     "1"      "1"      "2"      "2"  "3"  "3"           
[31,] "New York"       "3"      "3"      "1"      "1"  "1"  "2"           
[32,] "North Carolina" "1"      "1"      "3"      "3"  "1"  "1"           
[33,] "North Dakota"   "2"      "2"      "1"      "1"  "1"  "2"           
[34,] "Ohio"           "1"      "1"      "2"      "1"  "2"  "4"           
[35,] "Oklahoma"       "1"      "1"      "3"      "1"  "2"  "1"           
[36,] "Oregon"         "1"      "1"      "2"      "1"  "3"  "4"           
[37,] "Pennsylvania"   "1"      "1"      "2"      "1"  "2"  "4"           
[38,] "Rhode Island"   "1"      "1"      "2"      "1"  "1"  "4"           
[39,] "South Carolina" "1"      "1"      "3"      "3"  "1"  "1"           
[40,] "South Dakota"   "3"      "2"      "1"      "1"  "2"  "2"           
[41,] "Tennessee"      "1"      "1"      "3"      "1"  "2"  "4"           
[42,] "Texas"          "1"      "1"      "3"      "1"  "3"  "1"           
[43,] "Utah"           "3"      "1"      "2"      "1"  "3"  "3"           
[44,] "Vermont"        "3"      "3"      "1"      "1"  "1"  "2"           
[45,] "Virginia"       "1"      "1"      "2"      "3"  "2"  "4"           
[46,] "Washington"     "1"      "2"      "2"      "1"  "3"  "4"           
[47,] "West Virginia"  "1"      "1"      "2"      "3"  "2"  "4"           
[48,] "Wisconsin"      "3"      "3"      "1"      "1"  "2"  "2"           
[49,] "Wyoming"        "2"      "2"      "1"      "3"  "3"  "2"           

CLUSTER SENZA PDSI

std_multi_cluster<- scale(multi_cluster[,-c(1,6)])
dataset.e <- dist(std_multi_cluster, method = 'euclidean') #no method -> euclidean (default)

  dataset.es <- hclust(dataset.e, method = 'single') 
  dataset.ea <- hclust(dataset.e, method = 'average')
  dataset.ec <- hclust(dataset.e, method = 'complete')
  dataset.ew <- hclust(dataset.e, method = 'ward.D2')
  
  #plot of dendograms
  par(mfrow=c(1,3))
  plot(dataset.es, main='euclidean-single', hang=-0.1, xlab='', labels=F, cex=0.6, sub='')
  plot(dataset.ec, main='euclidean-complete', hang=-0.1, xlab='', labels=F, cex=0.6, sub='')

  plot(dataset.ea, main='euclidean-average', hang=-0.1, xlab='', labels=F, cex=0.6, sub='')

  plot(dataset.ew, main='euclidean-ward', hang=-0.1, xlab='', labels=F, cex=0.6, sub='')

  
  #cutting dendograms: (with k=2 fixed)
  cluster.ec <- cutree(dataset.ec, k=3) # euclidean-complete:
  cluster.ea <- cutree(dataset.ea, k=3) # euclidean-average:
  cluster.es <- cutree(dataset.es, k=3) # euclidean-simple:
  cluster.ew <- cutree(dataset.ew, k=4) # euclidean-simple:

  
  
  # Let's give a mark to the algorithms: did they aggregate coherently with
  # the dissimilarity matrix or not?
  # compute the cophenetic matrices 
  coph.es <- cophenetic(dataset.es)
  coph.ec <- cophenetic(dataset.ec)
  coph.ea <- cophenetic(dataset.ea)
  coph.ew <- cophenetic(dataset.ew)

  
  # compute cophenetic coefficients (<-> corr(D,C)) D:dist mat; C:coph dist mat
  es <- cor(dataset.e, coph.es)
  ec <- cor(dataset.e, coph.ec)
  ea <- cor(dataset.e, coph.ea)
  ew <- cor(dataset.e, coph.ew)

  
  c("Eucl-Single"=es,"Eucl-Compl."=ec,"Eucl-Ave."=ea, "Eucl-War."=ew)

Eucl-Single Eucl-Compl.   Eucl-Ave.   Eucl-War. 
  0.6094244   0.5573119   0.7680538   0.5700928 

cluster_index

      state            temp_min temp_max temp_avg prec pdsi multi_all_ward
 [1,] "Alabama"        "1"      "1"      "3"      "3"  "1"  "1"           
 [2,] "Alaska"         "2"      "3"      "1"      "1"  NA   "2"           
 [3,] "Arizona"        "1"      "1"      "3"      "2"  "3"  "3"           
 [4,] "Arkansas"       "1"      "1"      "3"      "1"  "2"  "1"           
 [5,] "California"     "1"      "1"      "3"      "1"  "3"  "3"           
 [6,] "Colorado"       "3"      "1"      "2"      "1"  "3"  "2"           
 [7,] "Connecticut"    "1"      "1"      "2"      "1"  "1"  "4"           
 [8,] "Delaware"       "1"      "1"      "2"      "3"  "1"  "4"           
 [9,] "Florida"        "1"      "1"      "3"      "1"  "3"  "1"           
[10,] "Georgia"        "1"      "1"      "3"      "3"  "1"  "1"           
[11,] "Idaho"          "2"      "2"      "1"      "1"  "3"  "2"           
[12,] "Illinois"       "1"      "1"      "2"      "1"  "2"  "4"           
[13,] "Indiana"        "1"      "1"      "2"      "1"  "2"  "4"           
[14,] "Iowa"           "3"      "2"      "1"      "1"  "2"  "2"           
[15,] "Kansas"         "1"      "1"      "2"      "1"  "2"  "1"           
[16,] "Kentucky"       "1"      "1"      "2"      "1"  "2"  "4"           
[17,] "Louisiana"      "1"      "1"      "3"      "1"  "2"  "1"           
[18,] "Maine"          "3"      "3"      "1"      "1"  "1"  "2"           
[19,] "Maryland"       "1"      "1"      "2"      "3"  "2"  "4"           
[20,] "Massachusetts"  "1"      "1"      "2"      "1"  "1"  "4"           
[21,] "Michigan"       "3"      "3"      "1"      "1"  "2"  "2"           
[22,] "Minnesota"      "3"      "2"      "1"      "1"  "2"  "2"           
[23,] "Mississippi"    "1"      "1"      "3"      "1"  "2"  "1"           
[24,] "Missouri"       "1"      "1"      "2"      "1"  "2"  "4"           
[25,] "Montana"        "2"      "2"      "1"      "1"  "3"  "2"           
[26,] "Nebraska"       "3"      "2"      "2"      "1"  "2"  "2"           
[27,] "Nevada"         "1"      "1"      "2"      "1"  "3"  "3"           
[28,] "New Hampshire"  "3"      "3"      "1"      "1"  "1"  "2"           
[29,] "New Jersey"     "1"      "1"      "2"      "1"  "1"  "4"           
[30,] "New Mexico"     "1"      "1"      "2"      "2"  "3"  "3"           
[31,] "New York"       "3"      "3"      "1"      "1"  "1"  "2"           
[32,] "North Carolina" "1"      "1"      "3"      "3"  "1"  "1"           
[33,] "North Dakota"   "2"      "2"      "1"      "1"  "1"  "2"           
[34,] "Ohio"           "1"      "1"      "2"      "1"  "2"  "4"           
[35,] "Oklahoma"       "1"      "1"      "3"      "1"  "2"  "1"           
[36,] "Oregon"         "1"      "1"      "2"      "1"  "3"  "4"           
[37,] "Pennsylvania"   "1"      "1"      "2"      "1"  "2"  "4"           
[38,] "Rhode Island"   "1"      "1"      "2"      "1"  "1"  "4"           
[39,] "South Carolina" "1"      "1"      "3"      "3"  "1"  "1"           
[40,] "South Dakota"   "3"      "2"      "1"      "1"  "2"  "2"           
[41,] "Tennessee"      "1"      "1"      "3"      "1"  "2"  "4"           
[42,] "Texas"          "1"      "1"      "3"      "1"  "3"  "1"           
[43,] "Utah"           "3"      "1"      "2"      "1"  "3"  "3"           
[44,] "Vermont"        "3"      "3"      "1"      "1"  "1"  "2"           
[45,] "Virginia"       "1"      "1"      "2"      "3"  "2"  "4"           
[46,] "Washington"     "1"      "2"      "2"      "1"  "3"  "4"           
[47,] "West Virginia"  "1"      "1"      "2"      "3"  "2"  "4"           
[48,] "Wisconsin"      "3"      "3"      "1"      "1"  "2"  "2"           
[49,] "Wyoming"        "2"      "2"      "1"      "3"  "3"  "2"           
      multi_all_avg multi_nopdsi_ward multi_nopdsi_avg
 [1,] "1"           "1"               "1"             
 [2,] "2"           "2"               "2"             
 [3,] "3"           "3"               "1"             
 [4,] "1"           "4"               "3"             
 [5,] "3"           "3"               "1"             
 [6,] "3"           "2"               "3"             
 [7,] "4"           "4"               "3"             
 [8,] "4"           "4"               "3"             
 [9,] "1"           "1"               "1"             
[10,] "1"           "1"               "1"             
[11,] "3"           "2"               "3"             
[12,] "4"           "4"               "3"             
[13,] "4"           "4"               "3"             
[14,] "4"           "2"               "3"             
[15,] "4"           "4"               "3"             
[16,] "4"           "4"               "3"             
[17,] "1"           "1"               "1"             
[18,] "4"           "2"               "3"             
[19,] "4"           "4"               "3"             
[20,] "4"           "4"               "3"             
[21,] "4"           "2"               "3"             
[22,] "4"           "2"               "3"             
[23,] "1"           "1"               "1"             
[24,] "4"           "4"               "3"             
[25,] "3"           "2"               "3"             
[26,] "4"           "2"               "3"             
[27,] "3"           "3"               "3"             
[28,] "4"           "2"               "3"             
[29,] "4"           "4"               "3"             
[30,] "3"           "3"               "3"             
[31,] "4"           "2"               "3"             
[32,] "1"           "4"               "3"             
[33,] "3"           "2"               "3"             
[34,] "4"           "4"               "3"             
[35,] "4"           "4"               "1"             
[36,] "3"           "4"               "3"             
[37,] "4"           "4"               "3"             
[38,] "4"           "4"               "3"             
[39,] "1"           "1"               "1"             
[40,] "4"           "2"               "3"             
[41,] "4"           "4"               "3"             
[42,] "1"           "3"               "1"             
[43,] "3"           "3"               "3"             
[44,] "4"           "2"               "3"             
[45,] "4"           "4"               "3"             
[46,] "4"           "4"               "3"             
[47,] "4"           "4"               "3"             
[48,] "4"           "2"               "3"             
[49,] "3"           "2"               "3"             

plot_ly(x=std_multi_cluster[,1], y=std_multi_cluster[,2], z=std_multi_cluster[,3], color=cluster.ea, pch=19)

No trace type specified:
  Based on info supplied, a 'scatter3d' trace seems appropriate.
  Read more about this trace type -> https://plotly.com/r/reference/#scatter3d
No scatter3d mode specifed:
  Setting the mode to markers
  Read more about this attribute -> https://plotly.com/r/reference/#scatter-mode
Warning: 'scatter3d' objects don't have these attributes: 'pch'
Valid attributes include:
'connectgaps', 'customdata', 'customdatasrc', 'error_x', 'error_y', 'error_z', 'hoverinfo', 'hoverinfosrc', 'hoverlabel', 'hovertemplate', 'hovertemplatesrc', 'hovertext', 'hovertextsrc', 'ids', 'idssrc', 'legendgroup', 'legendgrouptitle', 'legendrank', 'line', 'marker', 'meta', 'metasrc', 'mode', 'name', 'opacity', 'projection', 'scene', 'showlegend', 'stream', 'surfaceaxis', 'surfacecolor', 'text', 'textfont', 'textposition', 'textpositionsrc', 'textsrc', 'texttemplate', 'texttemplatesrc', 'transforms', 'type', 'uid', 'uirevision', 'visible', 'x', 'xcalendar', 'xhoverformat', 'xsrc', 'y', 'ycalendar', 'yhoverformat', 'ysrc', 'z', 'zcalendar', 'zhoverformat', 'zsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule', '_bbox'

No trace type specified:
  Based on info supplied, a 'scatter3d' trace seems appropriate.
  Read more about this trace type -> https://plotly.com/r/reference/#scatter3d
No scatter3d mode specifed:
  Setting the mode to markers
  Read more about this attribute -> https://plotly.com/r/reference/#scatter-mode
Warning: 'scatter3d' objects don't have these attributes: 'pch'
Valid attributes include:
'connectgaps', 'customdata', 'customdatasrc', 'error_x', 'error_y', 'error_z', 'hoverinfo', 'hoverinfosrc', 'hoverlabel', 'hovertemplate', 'hovertemplatesrc', 'hovertext', 'hovertextsrc', 'ids', 'idssrc', 'legendgroup', 'legendgrouptitle', 'legendrank', 'line', 'marker', 'meta', 'metasrc', 'mode', 'name', 'opacity', 'projection', 'scene', 'showlegend', 'stream', 'surfaceaxis', 'surfacecolor', 'text', 'textfont', 'textposition', 'textpositionsrc', 'textsrc', 'texttemplate', 'texttemplatesrc', 'transforms', 'type', 'uid', 'uirevision', 'visible', 'x', 'xcalendar', 'xhoverformat', 'xsrc', 'y', 'ycalendar', 'yhoverformat', 'ysrc', 'z', 'zcalendar', 'zhoverformat', 'zsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule', '_bbox'